Related papers: About nonlinear geometric optics
In its 60 years of existence, the field of nonlinear optics has gained momentum especially over the past two decades thanks to major breakthroughs in material science and technology. In this article, we present a new set of data tables…
We obtain an asymptotic solution for $\ep \to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\ep$, but with…
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
We justify supercritical geometric optics in small time for the defocusing semiclassical Nonlinear Schrodinger Equation for a large class of non-necessarily homogeneous nonlinearities. The case of a half-space with Neumann boundary…
The angular spectrum theory is applied to the nonlinear harmonic generation process in optical superlattices. Several explicit and analytical structure functions are deduced to design optical superlattices for various purposes. Employing…
In this article, we review the history, current status, physical mechanisms, experimental methods, and applications of nonlinear magneto-optical effects in atomic vapors. We begin by describing the pioneering work of Macaluso and Corbino…
In a companion paper (Jonsson and Westman, Class. Quantum Grav. 23 (2006) 61), a generalization of optical geometry, assuming a non-shearing reference congruence, is discussed. Here we illustrate that this formalism can be applied to a…
Nowadays the geometric approach in optics is often used to find out media parameters based on propagation paths of the rays because in this case it is a direct problem. However inverse problem in the framework of geometrical optics is…
A general definition of a linear connection in noncommutative geometry has been recently proposed. Two examples are given of linear connections in noncommutative geometries which are based on matrix algebras. They both possess a unique…
Throughout human history, people have used sight to learn about the world, but only in relatively recent times the science of light has been developed. Egyptians and Mesopotamians made the first known lenses out of quartz, giving birth to…
Numerical nonlinear algebra is a computational paradigm that uses numerical analysis to study polynomial equations. Its origins were methods to solve systems of polynomial equations based on the classical theorem of B\'ezout. This was…
We derive an asymptotic solution of the vacuum Einstein equations that describes the propagation and diffraction of a localized, large-amplitude, rapidly-varying gravitational wave. We compare and contrast the resulting theory of strongly…
The geometric phase of light is a fascinating phenomenon in optics and arises whenever there is a change in the polarization state of light. It is a fundamentally well-established concept and has recently found extensive applications,…
Nonlinear optical processes are vital for fields including telecommunications, signal processing, data storage, spectroscopy, sensing, and imaging. As an independent research area, nonlinear optics began with the invention of the laser,…
Recently, a lot of effort has been dedicated to developing next-generation optoelectronic devices based on two-dimensional materials, thanks to their unique optical properties that are significantly different from those of their bulk…
Nonlinear optics has long been a cornerstone of modern photonic technology, enabling a wide array of applications, from frequency conversion to the generation of ultrafast light pulses. Recent breakthroughs in two-dimensional (2D) materials…
Optical computing systems provide an alternate hardware model which appears to be aligned with the demands of neural network workloads. However, the challenge of implementing energy efficient nonlinearities in optics -- a key requirement…
It is shown that the geometrical optics limit of the Maxwell equations for certain nonlinear media with slow variation along one axis and particular dependence of dielectric constant on the frequency and fields gives rise to the…
We expose some simple facts at the interplay between mathematics and the real world, putting in evidence mathematical objects " nonlinear generalized functions" that are needed to model the real world, which appear to have been generally…
In this paper we develop a general concept of Lax operators on algebraic curves introduced in [1]. We observe that the space of Lax operators is closed with respect to their usual multiplication as matrix-valued functions. We construct the…